Question: Express your answer as a mixed number simplified to lowest terms. $7\dfrac{1}{9}-3\dfrac{3}{5} = {?}$
Solution: Find a common denominator for the fractions: $= {7\dfrac{5}{45}}-{3\dfrac{27}{45}}$ Convert ${7\dfrac{5}{45}}$ to ${6 + \dfrac{45}{45} + \dfrac{5}{45}}$ So the problem becomes: ${6\dfrac{50}{45}}-{3\dfrac{27}{45}}$ Separate the whole numbers from the fractional parts: $= {6} + {\dfrac{50}{45}} - {3} - {\dfrac{27}{45}}$ Bring the whole numbers together and the fractions together: $= {6} - {3} + {\dfrac{50}{45}} - {\dfrac{27}{45}}$ Subtract the whole numbers: $=3 + {\dfrac{50}{45}} - {\dfrac{27}{45}}$ Subtract the fractions: $= 3+\dfrac{23}{45}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{23}{45}$